Generalized Pareto distributions play an important role in re-liability, extreme value theory, and other branches of applied probability and statistics. This family of distribution includes exponential distribution, Pareto distribution, and Power distribution. In this paper we establish some recurrences relations satisfied by the quotient moments of the upper record values from the generalized Pareto distribution. Further a char-acterization of this distribution based on recurrence relations of quotient moments of record values is presented.

A variant of the global conjugate gradient method for solving general linear systems with multiple right-hand sides is proposed. This method is called as the global conjugate gradient linear least squares (Gl-CGLS) method since it is based on the conjugate gradient least squares method(CGLS). We present how this method can be implemented for the image deblurring problems with Neumann boundary conditions. Numerical experiments are tested on some blurred images for the purpose of comparing the computational efficiencies of Gl-CGLS with CGLS and Gl-LSQR. The results show that Gl-CGLS method is numerically more efficient than others for the ill-posed problems.

The essential aim of this paper is to define weighted -Hardylittlewood-type maximal operator by means of -adic -invariant distribution on . Moreover, we give some interesting properties concerning this type maximal operator.

In this paper, we consider two kinds of the Levenberg-Marquardt method for solve a system of nonlinear equations. We use line search on every iteration to guarantee that the Levenberg-Marquardt methods are globally convergent. Under mild conditions, we prove that while the de- scent condition can be satisfied at the iteration of the Levenberg-Marquardt method, the global convergence of the method can be established.

In this paper, we introduce more general concepts of regularity and S-unitality, that is, -regularity and -unitality and then give some examples in near-rings, also investigate their characterization and proper-ties.

In this paper, a turbidostat model with ratio-dependent growth rate and impulsive state feedback control is considered. We obtain sufficient conditions of the globally asymptotically stable of the system without impulsive state feedback control. We also obtain that the system with impulsive state feedback control has periodic solution of order one. Sufficient conditions for existence and stability of periodic solution of order one are given. In some cases, it is possible that the system exists periodic solution of order two. Our results show that the control measure is effective and reliable.

The semilocal convergence of a third order iterative method used for solving nonlinear operator equations in Banach spaces is established by using recurrence relations under the assumption that the second Fr´echet derivative of the involved operator satisfies the -continuity condition given by , , where, is a nondecreasing continuous real function for x > 0, such that . This condition is milder than the usual Lipschitz/Hlder continuity condition on . A family of recurrence relations based on two constants depending on the involved operator is derived. An existence-uniqueness theorem is established to show that the R-order convergence of the method is (2+), where . A priori error bounds for the method are also derived. Two numerical examples are worked out to demonstrate the efficacy of our approach and comparisons are elucidated with a known result.

Giuliano Antonini et al.(2008) have introduced the concept of extended acceptability and the results show that the extended acceptability structure has no effect on the exponential inequality except replacing a constant M

In literature, several strong designated verifier signature (SDVS) schemes have been devised using elliptic curve bilinear pairing and map-topoint (MTP) hash function. The bilinear pairing requires a super-singular elliptic curve group having large number of elements and the relative computation cost of it is approximately two to three times higher than that of elliptic curve point multiplication, which indicates that bilinear pairing is an expensive operation. Moreover, the MTP function, which maps a user identity into an elliptic curve point, is more expensive than an elliptic curve scalar point multiplication. Hence, the SDVS schemes from bilinear pairing and MTP hash function are not efficient in real environments. Thus, a cost-efficient SDVS scheme using elliptic curve cryptography with pairingfree operation is proposed in this paper that instead of MTP hash function uses a general cryptographic hash function. The security analysis shows that our scheme is secure in the random oracle model with the hardness assumption of CDH problem. In addition, the formal security validation of the proposed scheme is done using AVISPA tool (Automated Validation of Internet Security Protocols and Applications) that demonstrated that our scheme is unforgeable against passive and active attacks. Our scheme also satisfies the different properties of an SDVS scheme including strongness, source hiding, non-transferability and unforgeability. The comparison of our scheme with others are given, which shows that it outperforms in terms of security, computation cost and bandwidth requirement.

In this paper we consider a model with demographics for sexually transmitted diseases (STDs) spread on scale-free networks. We derive the epidemic threshold, which is depend on the birth rate, the natural death rate and other parameters. The absence of a threshold in infinite scale-free network is proved. For a hard cut off scale-free network, we also analyze the stability of disease-free equilibrium and the persistence of STDs infection. Two immunization schemes, proportional scheme and targeted vaccination, are studied and compared. We find that targeted strategy is more effective on scale-free networks.

There exist many deterministic models for signaling pathways in systems biology. However the models do not consider the stochastic properties of the pathways, which means the models fit well with experimental data in certain situations but poorly in others. Incorporating stochasticity into deterministic models is one way to handle this problem. In this paper the way is used to produce stochastic models based on the deterministic differential equations for the published extracellular signal-regulated kinase (ERK) pathway. We consider strong convergence and stability of the numerical approximations for the stochastic models.

Pattabiraman and Paulraja [K. Pattabiraman, P. Paulraja, Vertex and edge PI indices of the generalized hierarchical product of graphs, Discrete Appl. Math. 160 (2012) 1376- 1384] obtained exact formulas for the vertex and edge PI indices of generalized hierarchical product of graphs. The aim of this note is to improve the main results of this paper.

In this paper, we investigate a priori error estimates and superconvergence of varitional discretization for nonlinear parabolic optimal control problems with control constraints. The time discretization is based on the backward Euler method. The state and the adjoint state are approximated by piecewise linear functions and the control is not directly discretized. We derive a priori error estimates for the control and superconvergence between the numerical solution and elliptic projection for the state and the adjoint state and present a numerical example for illustrating our theoretical results.

This note is concerned with the uniform -continuity of solution for the stochastic differential equations under Lipschitz condition and linear growth condition. Furthermore, uniform -continuity of the solution for the stochastic functional differential equation is given.

In this article, Adomian decomposition method (ADM), variation iteration method(VIM) and homotopy analysis method (HAM) for solving integro-differential equation with singular kernel have been investigated. Also,we study the existence and uniqueness of solutions and the convergence of present methods. The accuracy of the proposed method are illustrated with solving some numerical examples.

This paper mainly deals with the stochastic control system, the existence and uniqueness of solutions and the behavior of solutions are investigated. Firstly, we obtain sufficient conditions which guarantee the existence and uniqueness of solutions to the stochastic control system. And then, boundedness of the solution to the system is achieved under mean-square linear growth condition.

The multiplicative version of Wiener index (-index), proposed by Gutman et al. in 2000, is equal to the product of the distances between all pairs of vertices of a (molecular) graph G. In this paper, we first present some sharp bounds in terms of the order and other graph parameters including the diameter, degree sequence, Zagreb indices, Zagreb coindices, eccentric connectivity index and Merrifield-Simmons index for -index of general connected graphs and trees, as well as a Nordhaus-Gaddum-type bound for -index of connected triangle-free graphs. Then we study the behavior of -index upon the case when removing a vertex or an edge from the underlying graph. Finally, we investigate the extremal properties of -index within the set of trees and unicyclic graphs.

In this paper we investigate necessary conditions for the mirror algebra to be a -algebra (having the condition (D5), resp.) when (X, *, 0) is a d-algebra (having the condition (D5), resp.). Moreover, we obtain the necessary conditions for M(X) of a -algebra X to be a -algebra.

In this paper, we study the global stability and the existence of almost periodic solution of high-order Hopfield neural networks with distributed delays of neutral type. Some sufficient conditions are obtained for the existence, uniqueness and global exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques. An example is given to show the effectiveness of the proposed method and results.